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Re: [PrimeNumbers] prime k-tuples

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  • Phil Carmody
    ... Can you briefly explain what the last occurance represents. First occurance seems obvious, assuming it s the smallest w such that a tuple of with w can
    Message 1 of 3 , May 29, 2006
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      --- Tom <tom@...> wrote:
      > The latest info has been posted.
      >
      > Current information shows the difference growing
      > at a rate of one additional prime every increase
      > of 267 in width when looked at as a linear best fit,
      > but the growth rate is tending to be concave up.
      >
      > A plot of k(width)-pi(width) versus width is at
      > www.opertech.com/primes/trophy.jpg
      > were k(width) is the number of primes in a interval.
      >
      > A list of first occurances (width) is at
      > www.opertech.com/primes/trophycase.html

      Can you briefly explain what the 'last occurance' represents. First occurance
      seems obvious, assuming it's the smallest w such that a tuple of with w can be
      found where k(w)-pi(w) takes the stated value, k(w) being the count of slots in
      the tuple. Is the last occurance simply the w such that all larger w have a
      currently known tuple with the stated delta?

      That graph has a wonderful hockey-stick shape. I can think of no heuristic
      which would suggest that it either ought to be asymptotically linear, or
      concave up. Convex up would, however, surprise me, but again I couldn't explain
      why.

      Phil

      Phil

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